Forces, for the exam.

Part 1Scalars and vectors

A scalar quantity has size (magnitude) only. A vector quantity has size and direction. That direction is the whole point — it's why velocity and speed aren't the same thing.

We draw a vector as an arrow: the length shows the size, and the way it points shows the direction. A force is a vector, so it always has both a strength and a direction.

A force is a push or a pull on an object, caused by it interacting with something else. Forces come in two families. A contact force needs the objects to be touching. A non-contact force acts at a distance, with no touching at all.

Part 2Mass and weight

Mass is the amount of matter in an object, measured in kilograms (kg). It never changes — you have the same mass on the Moon as on Earth. Weight is the force of gravity pulling on that mass, measured in newtons (N). Weight changes if the gravitational field strength changes.

Weight acts straight down from a single point called the centre of mass. Weight is directly proportional to mass: double the mass, double the weight.

Part 1Combining forces in a line

Usually several forces act on an object at once. You can always replace them with a single force that has the same effect — the resultant force.

When forces act along the same line, just add them up, treating one direction as positive and the opposite as negative. Forces the same way add; forces opposite ways subtract. A free body diagram shows the object as a dot or box with an arrow for each force acting on it.

Part 2Forces at angles

When forces don't act along the same line, a single arrow can still represent their combined effect. On Higher tier you also need to do the reverse — split one force into two.

Part 1Work means transferring energy

Work is done whenever a force moves an object through a distance. Doing work transfers energy — the work done equals the energy transferred. Work is measured in joules (J), the same unit as energy.

The distance must be measured along the line of the force. One joule of work is done when a force of 1 N moves an object 1 m in the direction of the force, so 1 J = 1 N m.

Part 2Work against friction

When you do work against friction, the energy you transfer doesn't disappear — it ends up in the thermal store of the object and its surroundings. That's why rubbing your hands together warms them, and why brakes and tyres get hot.

So work done against friction causes a rise in temperature. The energy is dissipated, spread out and harder to use — but it is still conserved.

Part 1Stretching springs

To change the shape of a spring you need more than one force — one to stretch each end (or to compress, or to bend). With one force the spring would just move off, not deform.

Up to a point, the extension is directly proportional to the force — that's Hooke's law. Stretch it too far and you pass the limit of proportionality, where the line stops being straight.

Deformation is elastic if the object returns to its original shape when the force is removed. It's inelastic if it stays permanently stretched or bent. The work done in stretching a spring (elastically) is stored in its elastic potential store.

Part 2Measuring the relationship

Part 1The words, and one equation

Distance is how far you travel — a scalar, no direction. Displacement is the straight-line distance and direction from start to finish — a vector. Walk a full lap of a track and your distance is the lap length, but your displacement is zero.

Speed is a scalar (how fast, no direction). Velocity is speed in a stated direction — a vector. So an object can move at constant speed but changing velocity, if its direction keeps changing (like a car going round a roundabout).

Part 2Distance–time graphs

On a distance–time graph, the gradient (slope) is the speed. A steeper line means faster; a horizontal line means stationary; a curve means the speed is changing.

Part 1The rate of change of velocity

Acceleration is how quickly velocity changes, measured in metres per second squared (m/s²). Speeding up is a positive acceleration; slowing down is a negative acceleration, also called deceleration.

Part 2Velocity–time graphs

On a velocity–time graph, the gradient is the acceleration and the area under the line is the distance travelled. A flat line means constant velocity (zero acceleration); a straight slope means constant acceleration.

Part 1The first and second laws

Newton's first law: if the resultant force on an object is zero, a still object stays still and a moving object keeps the same velocity (same speed and direction). So a car at steady speed has balanced forces. To change velocity, you need an unbalanced force.

The tendency of an object to keep its state of rest or motion is its inertia. Newton's second law tells you how much it accelerates: the acceleration is proportional to the resultant force and inversely proportional to the mass.

Part 2The third law & momentum

Newton's third law: whenever two objects interact, they exert equal and opposite forces on each other. If you push a wall, the wall pushes back on you just as hard. The two forces are the same size, opposite direction, and act on different objects.

Part 1Thinking + braking

The stopping distance is the total distance a vehicle travels from the moment a hazard appears to the moment it stops. It is made of two parts:

Thinking distance — how far the car travels during the driver's reaction time, before the brakes are even touched. Braking distance — how far it travels once the brakes are applied, while it slows to a stop.

Part 2The factors, and braking forces

Thinking distance increases with a longer reaction time — caused by tiredness, alcohol or drugs, and distractions like phones. (Typical reaction times are around 0.2–0.9 s.)

Braking distance increases with higher speed, poor road conditions (wet or icy — less friction), and poor vehicle condition (worn brakes or bald tyres).

When the brakes are applied, friction at the brake pads does work against the wheels. This transfers energy from the car's kinetic store to the thermal store of the brakes, so the brakes get hot. A larger braking force means a greater deceleration — but very large decelerations can cause skidding and brakes to overheat.